Correlation and Prediction of Redox Potentials of Hydrogen Evolution

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The Correlation and Prediction of Redox Potentials of Hydrogen Evolution Mononuclear Cobalt Catalysts via Molecular Electrostatic Potential: A DFT Study Bai Amutha Anjali, Fareed Bhasha Sayyed, and Cherumuttathu H Suresh J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b11543 • Publication Date (Web): 02 Feb 2016 Downloaded from http://pubs.acs.org on February 9, 2016

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The Journal of Physical Chemistry

The Correlation and Prediction of Redox Potentials of Hydrogen Evolution Mononuclear Cobalt Catalysts via Molecular Electrostatic Potential: A DFT Study Bai Amutha Anjali,†‡ Fareed Bhasha Sayyed† and Cherumuttathu H. Suresh*†‡ ‡

Chemical Sciences and Technology Division, Academy of Scientific & Innovative Research (AcSIR), CSIR-National Institute for Interdisciplinary Science and Technology, Trivandrum 695019, India ABSTRACT: Reduction potentials (E0) of six mononuclear cobalt catalysts (1 - 6) for hydrogen evolution reaction and electron donating/withdrawing effect of nine X-substituents on their macrocyclic ligand are reported at solvation effect-included B3P86/6311+G** level of density functional theory. The electrostatic potential at the Co nucleus (VCo) is found to be a powerful descriptor of the electronic effect experienced by Co from the ligand environment. The VCo values vary substantially with respect to the nature of macrocycle, type of apical ligands, nature of substituent and oxidation state of the metal center. Most importantly, VCo values of both the oxidized and reduced states of all the six complexes show strong linear correlation with E0. The correlation plots between VCo and E0 provide an easy-to-interpret graphical interpretation and quantification of the effect of ligand environment on the reduction potential. Further, on the basis of a correlation between the relative VCo and relative E0 values of a catalyst with respect to the CF3-substituted reference system, the E0 of any X-substituted 1 - 6 complexes is predicted.

INTRODUCTION Mononuclear cobalt complexes of tetraazamacrocyclic ligands are promising class of hydrogen evolving electro catalysts, known to work at modest over potential.1-10 Recently Solis and Hammes-Schiffer studied the effect of substituents on tuning the reduction potentials (E0) of cobalt diglyoxime complex referred to here as 1-X.11 Solis and Hammes-Schiffer showed that E0 and pKa values of 1-X correlates linearly to the Hammett substituent constant. The E0 becomes more negative with increase in the electron donating character of the substituent. Theoretical calculation of E0 to the experimental accuracy is very difficult to achieve as it demands very accurate estimation of thermodynamic parameters for both oxidized and reduced forms of the complex. This becomes even more challenging for various substituted cases as the finer substituent effects may lead to subtle variations in E0 values. Solis and Hammes-Schiffer's work suggests that E0 for 1-X complex can be predicted with a knowledge of substituent effect. Among the theoretically derived properties useful for the interpretation and quantification of substituent effects in molecular systems, the topographical and surface features of molecular electrostatic potential (MESP) have been widely used. The MESP can be experimentally determined from electron density data derived from X-ray diffraction studies on crystals whereas being a one electron property, its accurate calculation is rather easy with theoretical methods implemented in many of the standard ab initio/DFT program packages. The use of the theoretically derived MESP to understand molecular reactivity has been pioneered by the works of Tomasi,12 Pullman,13 Politzer14-19 and Gadre20-23. Recently the works of Wheeler and Houk 24-28 have contributed to the growth of this area. In many of the studies from our group, we have shown that MESP based analysis is useful to interpret and quantify resonance

effect,29 inductive effect,30 substituent effects,31-32 trans influence,33 cation-π interactions,34-36 lone pair-π interactions,37 non-covalent interactions including a large variety of hydrogen bonds,38 aromatic character of benzenoid hydrocarbons,3940 stereoelectronic features of ligands in organometallic/inorganic chemistry41-46 etc. Very recently we have shown that the MESP minimum (Vmin) at the hydride ligand or MESP at the hydride nucleus (VH) of a metal hydride complex can quantify the hydricity of the complex.47 In general, Vmin of an electron rich site and MESP value at the nearest nucleus show similar linear trend with respect to the electron donating/withdrawing character of a substituent. In case of electron deficient systems where Vmin is not observed, MESP at a convenient nucleus (typically the reaction centre) is useful to determine the substituent effect. Certainly, the MESP based descriptors have emerged as a sensitive electronic parameters in the study of molecular reactivity and related phenomena.15 More than a decade ago Suresh and Koga44 showed a strong linear relationship between Vmin at the lone pair region of PR3 ligands and Tolman electronic parameter. On the basis of this correlation, Vmin has been used as a convenient electronic parameter to gauge the electron donating effect of PR3 ligands in coordination complexes. They also derived a linear correlation between Vmin and the experimental enthalpy change reported by Fernandez et al.48 for the electrochemical couple ηCp(CO)(PR3)(COMe)Fe+/η-Cp(CO)(PR3)(COMe)Fe0. Barring this study, a MESP based analysis of E0 of a molecular system is yet to be reported. Herein we show that E0 of an organometallic complex can be finely tuned by monitoring the MESP at the nucleus of the metal center. In a recent paper, Peters et al49 reported electro catalytic hydrogen evolution in acidic water for six methyl substituted cobaloxime systems, viz. 1-X, [2X]2+, 3-X, [4-X]3+, [5-X]3+ and 6-X (Figure 1). These systems are selected for our study and in addition to X = CH3, the ef-

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fect of CN, CF3, Cl, H, F, OCH3, OH and NH2 on the tetraazamacrocycle to modulate E0 is considered. 2+

NCCH3 F F

X B

O N N

N O

X H3 CCN

N

F

F

X

X

OH2

N O

H

X

Br

3-X

3+ OH2

Br

3+ X

X

X N

N Co

N O Co

N X

X

N

X

N

X OH2

X

N

HO H

N O

[2-X]2+

1-X

X

X

N O Co

B

Br

OH2 X

N

N O Co

O

X

X

N

N

Co

O N N

H

N O Co

O

N

H

N O

N

X

X

H2 O

OH2

H

X

[5-X]3+

[4-X] 3+

X OH2

6-X

Figure 1. Cobalt complexes of tetraazamacrocyclic ligands (X = CN, CF3, Cl, H, F, CH3, OCH3, OH and NH2).

METHODOLOGY Isodesmic reaction method by incorporating a reference11, 50-53 is used to calculate reduction potential (E0). In this method, a half cell reaction with a known experimental E0 is taken as the reference (E0(ref)). The half cell reaction for which E0 has to be calculated is combined with the reference to form the isodesmic reaction. E0 is calculated using the Nernst equation, E0 = ∆Gsolv/nF where F is the Faraday constant (23.06 kcal mol-1 V1 ) and n is the number of electrons involved (n = 1 for the reactions studied). In this approach the free energy contribution of electron gets cancelled.11, 53 We use the experimentally reported3-4 E0 (-0.55 vs. standard calomel electrode (SCE)) of CoII (dmgBF2)2L2 (dmg = dimethylglyoxime) as E0(ref) in the isodesmic reaction approach (eqs. 1-4) to calculate the reduction potential of 1-X systems. CoII(dmgBF2)2L2 + e- → [CoI(dmgBF2)2L]- + L where L is CH3CN. -

(1)

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the reference reaction, the oxidized and reduced forms of all 26 systems have been studied using full ligand environment. [CoIII(dmgBF2)2L2]+ + e- → CoII(dmgBF2)2L2 (5) where L is CH3CN. For all computations, B3P86/6-311+G** density functional theory (DFT)54-58 is used as implemented in the Gaussian0959 since a previous benchmark study by Solis and Hammes-Schiffer suggests this basis set and functional to reproduce experimental geometries.11, 51 The oxidized and reduced species were optimized in the gas phase and also verified that all are minima by vibrational frequency calculation. Complexes with unpaired electrons, viz. 1-X, [2-X]+, [3-X]-, [4-X]2+, [5X]2+ and [6-X]- are computed with the unrestricted UB3P86/6311+G** level of theory in doublet state. Complex [1-X′′]- is having CoI metal centre and it is found to be more stable in low spin singlet state than in high spin state. The solvation free energy, ∆Gsolv is obtained using self-consistent reaction ﬁeld (SCRF) approach using ‘solvation model density’ (SMD) method60. SMD is found to be reliable in calculating free energy.61-62 Acetonitrile is used as the solvent since most of the electrochemical experiments have been performed in this solvent. Further, E0(ref) values used in the isodesmic scheme correspond to experiments conducted in acetonitrile solvent. The standard equation to calculate the molecular electrostatic potential (V(r)) at a point r is N

V (r ) = ∑ A

ZA ρ(r ' )d 3r' −∫ r − RA r − r'

(6)

Here, ZA is the charge on the nucleus A which is located at the position RA, ρ(r′) is the electron density function and N is the total number of nuclei in the molecule. The MESP at the nucleus A (VA) is obtained by removing the nuclear contribution due to ZA from the above eqn. The MESP calculation is done with Gaussian09 and VA is directly taken from the Gaussian output file. Since the metal centre experiences the total effect of all the ligands, VA of the cobalt nucleus (designated as VCo) is analyzed for the quantification of the effects of ligands and substituents on the redox potential values.

RESULTS AND DISCUSSION

-

1-X + e → [1-X′′] + L Combining (1) and (2) gives the isodesmic reaction

(2)

CoII(dmgBF2)2L2 + [1-X′′]- → [CoI(dmgBF2)2L]- + 1-X

(3)

E0 = -∆Gsolv/nF + E0(ref) (4) 0(ref) where E is -0.55 V and ∆Gsolv is the free energy change of the isodesmic reaction (3). It may be noted that, a ligand loss from 1-X leading to [1-X′′]- has to be considered to develop the isodesmic scheme. For [2-X]2+, 3-X, [4-X]3+, [5-X]3+ and 6-X systems, CoIII to CoII reduction occurs. The reference reaction to develop the isodesmic scheme for these systems is given in eq. 5. The E0 0.20 V vs. SCE3 is experimentally known for this reference reaction which is used as the E0(ref) to calculate E0 for [2-X]2+, 3-X, [4-X]3+, [5-X]3+ and 6-X systems. It may be noted that the reference reaction for complexes 2-6 uses an experimental peak potential, which is not rigorously defined as E0 due to reaction kinetics that can shift the peak position in the cyclic voltammetry. However, it is reasonable to assume that these related complexes would behave similarly for the noncatalytic CoIII/II reduction. Since, no ligand loss is happening in

Structural details of optimized complexes Figure 2 shows optimized structures of the oxidized and reduced forms of the complexes 1-6 with X = H substitution. In 1-X, CoII center is hexacoordinated while the reduced CoI anion is pentacoordinated due to the ligand (acetonitrile) loss.3, 11 The metal center of all the oxidized and reduced forms of 25 systems is hexacoordinated as no ligand loss is observed which is desirable to develop the isodesmic scheme for CoIII/II reduction. In the case of reduced forms of 6-X systems wherein the X substituent is F, H, CH3, OH, OCH3 and NH2, the axial ligand water gets displaced from the metal coordination sphere to form hydrogen bonded adduct with the macrocycle. In such cases, the metal center is pentacoordinated while the rest (X substituent is CN, CF3 and Cl) show the normal hexacoordinated state of the metal center. In all the oxidized and reduced forms of the complexes, the average value of the equatorial Co-N distances (d1) fall in the narrow range of 1.86 – 1.96 Å. Nearly same


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1-H

[1-H′′]-

[4-H]3+

[4-H]2+

3-H

[2-H]2+

[3-H]+

[2-H]

[5-H]3+

[5-H]2+

6-H

[6-H]-

Figure 2. Optimized geometries of the oxidized and reduced forms of the complexes 1 - 6 with X = H, at B3P86/6-311+G** level of theory (distances in Å).


The Journal of Physical Chemistry d1 values are shown by both oxidized and reduced forms of a particular case. In 1-X, the distance from metal centre to axial ligand (d2), CoI-Laxial (1.92 Å) is significantly smaller compared to CoII-Laxial distance (2.24 Å) which can be attributed to the reduced coordination number of the former.3 In all other complexes where coordination number of the metal is unchanged during reduction, significant increase in d2 is observed in the reduced forms compared to the oxidized forms (Table S1 in Supporting Information). Reduction potential Table 1 shows calculated E0 values of all the complexes vs. SCE. For 1-X, the most electron withdrawing CN substitution gives CoII/I reduction potential 0.90 V whereas for the most electron donating substituent NH2, the reduction potential is 1.14 V. The E0 values of CF3, Cl, F, H, CH3, OCH3 and OH substituted 1-X are 0.57, 0.00, 0.37,-0.17,-0.55,-0.88 and -0.67 V, respectively. In general, E0 decreases as we move from electron withdrawing to electron donating substituents. This observation holds good for all the six systems studied herein and also suggests a linear correlation between Hammett substituent constant σp and E0 (Figure 3). Earlier, Solis and Hammes-Schiffer reported such a correlation for 1-X.11 We also note that E0 values obtained by us agree very well to those reported by Solis and Hammes-Schiffer using B3P86/6311+G** DFT in conjunction with the conductor-like polarizable continuum model (C-PCM) for solvation effects. The mean absolute deviation of our results with values reported by Hammes-Schiffer for matching eight systems is 0.052 V.11 6-X shows relatively weaker correlation between σp and E0 while the rest of the systems show correlation coefficient (r) above 0.94. We also note that E0 calculated in this work does not include the effect of external acid as protonation may cause significant differences in the calculated values, particularly those having O-H-O bridges (2, 3 and 6).63 All the E0 values of 3-X are negative, the least negative (-0.69 V) is for CN substitution while the most negative is for NH2 substitution (-1.84 V). The E0 values of [4-X]3+ are more positive compared to other complexes. For this complex, E0 is 1.24 V for X = CN and it decreases as the Hammett constant decreases and reaches to -0.38 V for X = NH2. 2.00 y = 1.234x + 0.506 ([4-X]3+) r = 0.943 y = 1.1806x + 0.2052 ([2-X]2+) r = 0.948 y = 1.5301x - 0.2361 (1-X) r = 0.983

1.50 1.00

E0 (V vs SCE)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.50 0.00

y = 0.5876x + 0.2487 r = 0.945 ([5-X]3+)

-0.50 -1.00

y = 0.604x - 0.760 (6-X) r= 0.854

-1.50

y = 0.879x - 1.320 (3-X) r = 0.940

-2.00 -2.50 -0.80

-0.30

0.20

0.70

1.20

1.70

σp

Figure 3. Correlation between Hammett constant (σp) of Xsubstituents and computed E0 of X-substituted 1 - 6 complexes. [5-X]3+ is also showing positive E0 except for the complex with NH2 substitution. Similar to 3-X, 6-X is having negative E0 for CoIII/II reduction for all the nine substituents. In the case of 6-X, CN substituent gives the least negative E0 -0.22 V while NH2 substituent gives the most negative E0 -1.13 V.

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Table 1. Computed reduction potentials (E0) of complexes 1 - 6 with various ‘X’ substituents (values in V vs. SCE). X

1-X

[2-X]2+

3-X

[4-X]3+

[5-X]3+

6-X

CN

0.90

0.98

-0.69

1.24

0.61

-0.22

CF3

0.57

0.82

-0.86

1.18

0.56

-0.46

Cl

0.00

0.55

-1.07

0.89

0.44

-0.79

F

0.37

0.54

-1.10

0.87

0.42

-0.54

H

-0.17

-0.01

-1.54

0.31

0.16

-0.88

CH3

-0.55

-0.25

-1.70

0.04

0.02

-1.06

OCH3

-0.88

-0.15

-1.52

0.13

0.05

-1.00

OH

-0.67

-0.03

-1.55

0.30

0.14

-0.75

NH2

-1.14

-0.58

-1.84

-0.38

-0.15

-1.13

Molecular electrostatic potential analysis We have computed VCo values for all the systems at the gas phase as well as at the solvent phase for both the oxidized and reduced forms. The trends in the gas phase VCo values are very similar to the solvent phase VCo values. Hence, the more realistic solvent phase values are discussed and the gas phase data is presented in the supporting information. Table 2 depicts VCo values for the oxidized and reduced forms in the solvent phase. As the electron donating nature of the substituent increases, VCo becomes more negative suggesting a correlation between VCo and E0. All the systems show strong linear correlation between VCo and E0 as the r of the systems 1-X, [2-X]2+, 3-X, [4-X]3+, [5-X]3+and 6-X are 0.961, 0.978, 0.968, 0.965, 0.967 and 0.980 respectively (Figure 4). The mean absolute deviation (MAD) of the predicted E0 from the calculated E0 is 0.14, 0.09, 0.08, 0.13, 0.05 and 0.04 in V for 1-X, [2-X]2+, 3X, [4-X]3+, [5-X]3+and 6-X, respectively. They also suggest that the thermodynamic quantity E0 is primarily influenced by the ligand environment around the metal centre. Very similar results are obtained by correlating VCo values of the reduced forms against the E0 where r of the systems [1-X′′]-, [2-X]+, [3X]-, [4-X]2+, [5-X]2+ and [6-X]- is 0.972, 0.983, 0.979, 0.972, 0.979 and 0.982 respectively (Figure 5) while MAD of the corresponding predicted E0 is 0.13, 0.08, 0.07, 0.12, 0.04 and 0.05 V. The VCo versus E0 correlations are remarkable considering the fact that MESP, an electronic property evaluated from one point in the molecule is useful to make a good prediction on the thermodynamic quantity E0 of the system. MESP values also possess a thermodynamic connotation as by definition they represent the energy required to bring a unit test positive charge from infinity to the referred point. Bringing a test positive charge to the system suggests an oxidationlike process and also it implicates that MESP values are intimately related to the energetic behavior of a redox couple. The correlation plots obtained for reduced states are superior than those observed for the oxidized states. This observation make sense because the process of bringing a test positive charge to the reduced state correlates more accurately to the redox couple described herein than bringing a test positive charge to the oxidized state. The correlation plots in Figures 4 and 5 suggest that VCo is very sensitive to the nature of the ligand environment and oxidation state of the metal as they fall in different regions of the


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Table 2. Electrostatic potential at the metal centre (VCo) of oxidized and reduced complexes with various substituents in solution (values in au). Complex

CN

CF3

Cl

F

H

CH3

OCH3

OH

NH2

1-X

-122.0567

-122.0871

-122.1141

-122.1070

-122.1396

-122.1611

-122.1642

-122.1413

-122.1795

-121.6814

-121.7142

-121.7362

-121.7223

-121.7618

-121.7868

-121.7976

-121.7715

-121.8148

-122.0231

-122.0492

-122.0711

-122.0625

-122.0931

-122.1100

-122.1086

-122.0984

-122.1233

-121.5452

-121.5746

-121.5975

-121.5788

-121.6161

-121.6470

-121.6645

-121.6295

-121.6835

[2-X]

2+

3-X [4-X]

3+

[5-X]

3+

-121.6002

-121.6144

-121.6248

-121.6180

-121.6345

-121.6484

-121.6610

-121.6452

-121.6667

6-X

-121.9965

-122.0266

-122.0498

-122.0414

-122.0789

-122.0961

-122.0899

-122.0722

-122.1066

[1-X′′]-

-122.1810

-122.2192

-122.2631

-122.2673

-122.2943

-122.3201

-122.3148

-122.3063

-122.3423

[2-X]+

-121.9196

-121.9534

-121.9804

-121.9779

-122.0108

-122.0322

-122.0327

-122.0219

-122.0577

[3-X]-

-122.2005

-122.2301

-122.2538

-122.2528

-122.2812

-122.2945

-122.2880

-122.2829

-122.3032

[4-X]2+

-121.7851

-121.8171

-121.8464

-121.8407

-121.8708

-121.8985

-121.9125

-121.8888

-121.9379

[5-X]2+

-121.8419

-121.8585

-121.8718

-121.8716

-121.8849

-121.8973

-121.9084

-121.8971

-121.9195

-122.1957

-122.2271

-122.2484

-122.2218

-122.2602

-122.2791

-122.2653

-122.2555

-122.2932

[6-X]

-

Figure 4. Correlation between VCo and computed E0 for oxidised forms of X-substituted 1-6 complexes in solvent.

Figure 5. Correlation between VCo and computed E0 for reduced forms of X-substituted 1-6 complexes in solvent. plotted area. Among all the systems, [4-X]3+ and [5-X]3+ show nearly identical correlation graphs for both oxidized and re-

duced forms. This indicates that the ligands though chemically very different in these systems provide nearly identical trend in ligand effect on the metal center. An inspection of the macrocyclic ligand of [4-X]3+ and [5-X]3+ shows that in both cases the ligand coordination to Co is satisfied by four nitrogen lone pairs and two water molecules. Further, two of the N-to-N connection of the macrocycle is fulfilled by the – CH2CH2CH2– alkyl chain in both the cases. Therefore similarity in the nature Cu-N bonding can be attributed as a reason for the similar electronic effect experienced by [4-X]3+ and [5X]3+ leading to similar behavior for VCo versus E0 plot. The macrocycle in [4-X]3+ is more effective for obtaining higher reduction potential as the E0 values of this system is almost double than that of [5-X]3+. Ligand environment of [2-X]2+ though identical to [4-X]3+, the macrocycle of the former has –O-H-O– unit for N-to-N connections compared to –CH2CH2CH2– unit in the latter. Since Co in [2-X]2+ bears less positive charge than [4-X]3+, VCo value of the former is more negative than the latter. Almost same amount of change in VCo value of [2-X]2+ compared to [4-X]3+ is observed for all the substituents. This can be immediately noticed from the correlation plots as the correlation line obtained for [2-X]2+ is nearly parallel to that of [4-X]3+ for both oxidized and reduced forms. This result also suggest that the influence of ligand environment on E0 is very similar for [2-X]2+, [4-X]3+ and [5-X]3+. The E0 values of [2-X]2+ lie in between that of [4-X]3+ and [5-X]3+. In the case of 3-X, the macrocyclic ligand is same as that of [2-X]2+ except for an OH substituent present in the alkyl chain. Since 3-X is neutral, it shows more negative VCo values than [2-X]2+. It is noteworthy that E0 values of 3-X is negative for all the substituents. This may be attributed to anionic Brligands in 3-X which can provide more electron density to the metal compared to the neutral H2O in [2-X]2+. Compared to 3X, 6-X has two –O-H-O- units to make the N-to-N connectivity for the macrocycle. Further, 6-X has one Br- and one H2O ligand compared to two Br- in 3-X suggesting less negative VCo values for the former system compared to the latter. The VCo values in Tables S2 and S3 (Supporting Information) indicate that the oxidized and reduced forms of 6-X is



Table 3. ΔE0 (in V) and ΔVCo (in au) values based on CF3-substituded reference for the reduced state of X-substituted 1-6 systems in solvent. CN

CF3

Cl

F

H

CH3

OCH3

OH

NH2

∆VCo [1-X′′]

-

-0.0382

0.0000

0.0440

0.0481

0.0751

0.1009

0.0947

0.0871

0.1232

[2-X]+

-0.0337

0.0000

0.0270

0.0245

0.0574

0.0789

0.0793

0.0685

0.1043

[3-X]

-

-0.0296

0.0000

0.0237

0.0227

0.0510

0.0644

0.0579

0.0528

0.0731

[4-X]

2+

-0.0321

0.0000

0.0293

0.0236

0.0537

0.0814

0.0954

0.0717

0.1208

[5-X]2+

-0.0166

0.0000

0.0132

0.0131

0.0263

0.0388

0.0499

0.0385

0.0609

[6-X]-

-0.0314

0.0000

0.0213

-0.0053

0.0331

0.0520

0.0382

0.0284

0.0661

∆E 1-X [2-X]

2+

3-X [4-X]

3+

0

-0.33

0.00

0.58

0.74

0.73

1.12

1.45

1.24

1.71

-0.16

0.00

0.27

0.28

0.83

1.07

0.97

0.85

1.40

-0.17

0.00

0.21

0.24

0.67

0.84

0.67

0.69

0.98

-0.07

0.00

0.29

0.30

0.87

1.14

1.05

0.87

1.55

[5-X]3+

-0.06

0.00

0.12

0.14

0.40

0.54

0.56

0.42

0.71

6-X

-0.24

0.00

0.33

0.08

0.42

0.60

0.54

0.29

0.66

11 – 28 and 4 – 21 kcal/mol, respectively less negative than the corresponding values of 3-X. The slope of the correlation line for 6-X is 8.193 for oxidized and 9.782 for the reduced forms which are smaller than the slope of the correlation lines obtained for the oxidized and reduced forms of 3-X, [2-X]2+, [4-X]3+ and [5-X]3+ (nearly a constant, ~11.6). This means that the second–O-H-O– bridge in 6-X is not very electronwithdrawing, and therefore its effects on VCo and thus E0 are not so pronounced. The improvement in the E0 values of 6-X by 28 – 68 % compared to 3-X can be mainly attributed to the change in the two electron donor ligands than the changes made in the macrocyclic ligand. Among the six types of hydrogen evolving electrocatalysts studied herein, 1-X is the most unique due to its two –OBF2-O– bridges to make the macrocyclic N-to-N connectivity. For the oxidized form of 1-X, VCo is more negative than 3-X by 19 – 33 kcal/mol whereas the reduced form is less negative compared to [3-X]- system by 7 – 21 kcal/mol except for X = NH2 where VCo is more negative by 1.1 kcal/mol. Unlike the neutral systems 3-X and 6-X, 1-X shows positive E0 values for electron withdrawing substitution on the macrocycle while the electron donating substitution yields negative E0 values. The macrocycle of 1-X is more sensitive to substitution than rest of the complex as it yields the highest difference of 2.04 V for the most electron withdrawing 1-CN and the most electron donating 1-NH2 systems. A General Correlation for Predicting Redox Potentials Though the correlation equations given in Figures 4 and 5 are useful to predict the redox properties of a given type of molecular complex using the MESP value at the metal center, a general correlation approach encompassing all the set of complexes is more powerful. To derive such a correlation, we use the relative value of VCo (ΔVCo) and relative value of E0 (ΔE0) of a given type of complex with respect to a reference X-substituted complex. For instance, in the case of 1-X sys-

tems, with respect to 1-CF3 system as reference, ΔE0 of 1-NH2 and 1-CN are 1.71 and -0.33 V and the relative VCo values (ΔVCo) are 0.1232 and -0.0382 au respectively. Although one can select any X-substituted system as a reference, a screening study for all has shown that CF3-substituded reference gives the least variation (Supporting Information) in predicting E0 values for 1 - 6 systems. Further, as discussed before the data obtained for the reduced form provide better correlation than the oxidized form (Supporting Information). The ΔE0 and ΔVCo values based on CF3-substituted reference are given in Table 3 for the reduced state of 1 - 6 systems in solvent. Figure 6 shows a good linear correlation between ΔVCo and ΔE0 which suggests that if we know the E0 value of CF3-substituted system, E0 of any other substituted system can be predicted solely from the electrostatic potential at the cobalt nucleus of the reduced form of the complex. 1.9 1.5

ΔE0 in V vs. SCE

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ΔE0 = 12.567 (ΔVCo) r = 0.972

1.1 0.7 0.3 -0.1 -0.5 -0.06 -0.03

0

0.03

0.06

0.09

0.12

0.15

ΔVCo in au Figure 6. Linear correlation between the relative VCo (in au) and relative computed E0 (in V) values of the X-substituted complexes


Page 7 of 10

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1 - 6 with respect to those of the CF3-substituted 1 - 6 complexes in reduced state.

As per the correlation equation in Figure 6, ΔE0 of an Xsubstituted system is 12.567 times the ΔVCo. Therefore, E0 of the X-substituted system can be obtained by subtracting E0 of CF3-substituted system from 12.567 times ΔVCo of the Xsubstituted system. To further illustrate the use of this method in predicting E0 for unknown systems, we have computed VCo of 1-NO2, 2COF, 3-NO, 4-NCO, 5-CCl3, and 6-OCF3 in reduced form and obtained values -122.1961, -121.9660, -122.1798, 121.8929, -121.8989 and -122.2202 au, respectively. These values suggest that with respect to CF3-substituted system as reference, ΔVCo values of 1-NO2, 2-COF, 3-NO, 4-NCO, 5CCl3, and 6-OCF3 are -0.0231, 0.0126, -0.0503, -0.0758, 0.0404 and -0.0069 au, respectively. Hence, from the correlation equation in Figure 6, we can predict that E0 values for 1NO2, 2-COF, 3-NO, 4-NCO, 5-CCl3, and 6-OCF3 complexes are 0.86, 0.66, -0.23, 0.22, 0.05 and -0.38 V, respectively vs. SCE. We have also computed VCo values using two different methods, viz. the Minnesota DFT method M06L/6311+g(d,p)64 and Grimme's dispersion-corrected DFT method B97D/6-311+g(d,p)65 and tested the validity of the general correlation approach presented in Figure 6. The VCo values obtained from both these methods were more negative than B3P86/6-311+g(d,p) for all X-substituted 1 - 6 systems. Nevertheless, both the methods showed almost identical increasing trends in the negative character of VCo with respect to the increasing electron donating character of the substituent. Further, their ∆VCo versus ∆E0 correlation plots were in excellent agreement with B3P86/6-311+g(d,p) results (Supporting Information). CONCLUSION Six different mono nuclear cobalt complexes of tetraaza macrocyclic ligands used as catalysts for hydrogen evolution reaction have been studied with nine different substituents using density functional theory. Their reduction potentials are calculated using isodesmic reaction. MESP at the cobalt nucleus, VCo of both oxidized and reduced forms of all the complexes is also computed in gas phase and solvent. The VCo is found to be very sensitive to the ligand environment and oxidation state of the complexes. All the complexes showed excellent linear correlation between VCo and reduction potential E0 for both oxidized and reduced forms. The VCo versus E0 correlations suggest that MESP is an excellent tool to predict and fine tune the reduction potential of tetraza macrocyclic cobalt complexes. The slopes of the correlation plots obtained for [2-X]2+, 3X, [4-X]3+ and [5-X]3+ are found to be nearly a constant and suggest that the ligand environment of these complexes respond in a similar way to tune the value of E0. Among all the complexes, the ligand environment of 6-X comprising of two –O-H-O– bridges is the least sensitive to substituent effect on the macrocycle while that comprising of two –O-BF2-O– bridges in 1-X is the most sensitive to substituent effect to tune E0 values.63 A single correlation graph comprising of the VCo and E0 data, showing a linear relationship between the two quantities is obtained by taking their relative values with respect to a reference. This relationship is powerful to make a good prediction on the reduction potential of any type of cobalt complexes

considered in this study for any substituent X. The method to predict the E0 using MESP is very attractive considering that the calculation of the former requires computationally more demanding procedures to obtain accurate thermodynamic parameters.

ASSOCIATED CONTENT Supporting Information Coordinates and energies of optimized geometries, MESP table for all the complexes in both gas phase, MESP vs. E0 correlations in gas phase. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author E-mail: [email protected], Ph: +91-471-2515472 Note The authors declare no competing financial interest.

ACKNOWLEDGMENT This research is supported by the project CSC0129 by Council of Scientific and Industrial research (CSIR), India. B. A. thanks UGC, India, for a junior research fellowship.

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Table of Contents


10

Correlation and Prediction of Redox Potentials of Hydrogen Evolution

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